What is 2x^2+2y^2-2x+4y=45 ?

The solution to 2x^2+2y^2-2x+4y=45 is Circle with (a,b)=(1/2 ,-1),r=(sqrt(95))/2

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2x^2+2y^2-2x+4y=45

2 x^{2} + 2 y^{2} - 2 x + 4 y = 45

(a, b) = (\frac{1}{2}, - 1), r = \frac{95}{2}

Solution steps

2 x^{2} + 2 y^{2} - 2 x + 4 y = 45

Rewrite

2 x^{2} + 2 y^{2} - 2 x + 4 y = 45

in the form of the standard circle equation

(x - \frac{1}{2})^{2} + (y - (- 1))^{2} = (\frac{95}{2})^{2}

Therefore the circle properties are:

(a, b) = (\frac{1}{2}, - 1), r = \frac{95}{2}

2 x^{(2)} + 2 y^{(2)} - 4 x + 12 y - 12 = 0

x^{2} + y^{2} + 8 x + 8 y = - 16

3 x^{2} + 6 y + 3 y^{2} + 5 x - 15 = 0

x^{2} + y^{2} - 2 x + 4 y = 11

x^{2} + y^{2} - x + 3 y - \frac{15}{4} = 0

What is 2x^2+2y^2-2x+4y=45 ?
The solution to 2x^2+2y^2-2x+4y=45 is Circle with (a,b)=(1/2 ,-1),r=(sqrt(95))/2